Factorization Of Algebraic Expressions — Maths STD 9 — Question
Gujarat BoardEnglish MediumSTD 9MathsFactorization Of Algebraic Expressions2 Marks
Question
If $a+b+c=0$, then write the value of $a^3+b^3+c^3$.
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Answer
Recall the formula
$a^3+b^3+c^3-3 a b c=(a+b+c)\left(a^2+b^2+c^2-a b-b c-c a\right)$
When, $(a+b+c)=0$, we have
$a^3+b^3+c^3-3 a b c=0 \cdot\left(a^2+b^2+c^2-a b-b c-c a\right)$
$=0$
$a^3+b^3+c^3-3 a b c=0$
$\Rightarrow a^3+b^3+c^3=3 a b c$
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